Pg124 Framework:Number Magic square –arrange the digits 1 to What’s missing?(OHT)Arithmagons9 in a 3 by 3 array so that the total of the 3 ;3x is the same as x + x (OHT/worksheet)rows, 3 columns and 2 diagonals are all the + ?

‘How did you start? How did you continue?’;p + ? = 3p -? + 3q –q‘Are there any etc relationships between Draw out some useful strategieswhich will help A, B, C and D?’to solve the problem. For example:;All the digits will be used in the 3 rows (columns) and each row must have the same total. So the sum of 1 to 9 divided by 3 will give the magic number (15).;The mean/median/’middle’ number (5) will go in the centre to leave 4 pairs of numbers which sum to 10.AlgebraicMagic square –use the strategies as above to solve the algebraic magic square (see resource sheet.)Lesson 2Introduce the idea of Extend the laws of arithmetic to algebra and Invite pupils to demonstrate solving pyramids using solve pyramids by collecting like terms: Pg 22 how they have been solving 1 laws of arithmetic: Pg Yr 7 booklet.or 2 selected problems. 21 Yr 7 booklet –Pyramids (1)Draw the pyramid on board:‘What strategies have you n 6 8been using for solving the

? ?equations?’?

Oral and mentalMain teachingPlenary

‘I want the bottom number to be 34, what ‘Pyramids and equations’

should n be?’(OHT).

‘How did you work the number out?’

‘Can I write an equation using n?’‘Will the same strategy help

us to solve this pyramid?’

Pg 19 Yr 7 booklet: ‘Pyramids and equations

(1)’Q1 to 7.Link back to objectives:

Constructing and solving

linear equations. Explainthat

we are going to be working

on a strategy that will help us

to solve equations of this type

as well.

Lesson 3:Model ‘Solving linear equations using a number Invite pupils to share their Pg 18 Yr 8 booklet –line’ (OHT)responses to the questions

starter activity: Provide pupils with similar problems:‘Solving (at the front or on plastic equation from a pie linear equations using a number line’ wallets they have been chart, solved on a (worksheet.)working on)from the

number line.extension problem.

Extension: Pg 21Yr 8 booklet (Double pyramid)

‘Can you derive an equation to help solve the Review the objectives and

problem?’explain that we have been

‘What do you notice about the equation?’ using a number line to solve

(variables on both sides.)linear equations with a

‘How could you work out the value of t?variable on one side. Next

time, however, we aregoing

to use it to see if we can

solve equations with

variables on both sides as we

generated in this problem.

Lesson 4‘Was the number line useful Model the use of the number line to solve

in solving these equations?’ Ask pupils to generate equations of this type with variables on both

the linear equation sides (Pg 19 Year 8 booklet.) Ask pupils to use which would help this method to solve the double pyramid from Take feedback and ask one solve the double the previous lesson (or to verify their answer.)or two pupils to share their pyramid:solutions.

Pupils solve similar linear equations, for

n n 4example:Present the following three

? ?1.5x + 3 = 2x + 15equations:

?2.6x + 5 = 3x + 141.4x+ 7 = 2x + 13

? ?3.10x + 3 = 4x + 212.2x + 3 = 2x + 7

n 10 64.9x + 1 = 5x + 93.2x –1 = x + 9

5.4x + 7 = 2x + 13

‘Can anyone work out Ask pupils to use a number the value of n?’There are more problemsof increasing difficulty line to solve Q1 and spend a

on Pg 20 Year 8 booklet.few minutes on Q2 and Q3.

This task could be completed

for homework.

Lesson 5

(As Pgs 23 –25 in (As Pgs 23 –25 in the Year 8 booklet)(As Pgs 23 –25 in the Year the Year 8 booklet)8 booklet)

Complicating the Introducing the matching method.

expression.

K Wallis 10/04

OHT/Worksheet

Arithmagons

BA7

14

2

D9C

Some results Some relationshipsA B C D

OHT/Worksheet

Arithmagons

7

14

2

9

Some results Some relationshipsA B C D

Resource

Algebraic magic squares

a + 4b2a + b8a + 3b

5a + 2b7a + 6b7b

6a +9b4a + 5b3a +8b

Teacher note:

The sum of the expressions is 36a + 45b.

The magic number is (36a + 45b) ? 3 = 12a + 15b

The middle expression when put in order of ascending a terms is 4a + 5b

The other expressions can then be paired off e.g. 7b with 8a +

3b and a + 4b with 7a + 6b, which when added to the middle expression will give the magic number.

OHT

What’s missing?

E.g. 3x + y is the same as x + + +

1. a + 2b = 2a – + b +

2. 3x + 2y = 4x + y – +

3. p + = 3p – + 3q – q

4. 2a + = 3a – + b + 3c – b – c

5. + q – r = 3q + 4p – q – + 4r –– 2p

OHT

Pyramids and equations

8n3n

= 10 + 4n

OHT

Solving Linear equations using a number line

180 = 64 + 4x

180

x x x x 64

180 =

Name:______________________ Worksheet

Solving Linear equations using a number line

180 = 4x + 64 180 = x + x + x + x + 64

180 116 = x + x + x + x

29 = x

x x x x 64

Now try these the same way. i.e. Draw a number line. Show all your working. Underline your answer.